Sobolev training of thermodynamic-informed neural networks for smoothed elasto-plasticity models with level set hardening

TL;DR

This paper presents a novel deep learning framework for smoothed elastoplasticity models that leverages thermodynamic principles and level set methods to improve interpretability and prediction accuracy in cyclic stress simulations.

Contribution

It introduces a thermodynamically consistent neural network approach with level set hardening, capable of discovering classical and new hardening mechanisms from data.

Findings

More robust and accurate predictions of cyclic stress paths.

Outperforms black-box neural networks like GRU and CNN.

Enables interpretable and thermodynamically consistent modeling.

Abstract

We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as a smoothed stored elastic energy function, a yield surface, and a plastic flow that are evolved based on a set of deep neural network predictions. By recasting the yield function as an evolving level set, we introduce a machine learning approach to predict the solutions of the Hamilton-Jacobi equation that governs the hardening mechanism. This machine learning hardening law may recover classical hardening models and discover new mechanisms that are otherwise very difficult to anticipate and hand-craft. This treatment enables us to use supervised machine learning to generate models that are thermodynamically consistent, interpretable, but also exhibit excellent learning capacity. Using a 3D FFT solver to create a polycrystal database, numerical experiments are conducted and the implementations of each component of the models are individually verified. Our numerical experiments reveal that this new approach provides more robust and accurate forward predictions of cyclic stress paths than these obtained from black-box deep neural network models such as a recurrent GRU neural network, a 1D convolutional neural network, and a multi-step feedforward model.